Summary of Work: This project focuses on developing new statistical methods, and applying new and existing statistical techniques, to analyze data from laboratory animal studies. This year our research has dealt mainly with the use of functional restrictions to avoid restrictive parametric distributions, unrealistic biological assumptions, and expensive additional data. The endpoint of interest in a typical rodent carcinogenicity experiment is the tumor incidence rate, which reflects the age-specific rate at which new tumors develop. Unfortunately, most tumors are not observable in live animals and thus simple estimates of the tumor onset rate are not available. The basic tumor onset/death model has three states and three rates at which animals move between states. The three states are alive without a tumor, alive with a tumor, and dead. The three transition rates are the tumor incidence rate, the death rate for animals with a tumor, and the death rate for animals without a tumor. Most analyses either impose parametric distributions on some or all of the transition rates, or else assume that tumors are rapidly lethal or strictly nonlethal, or else require additional data such as cause-of-death assessments or interim sacrifices. Our research concentrates on an alternative approach that places constraints on the relationship between the death rates for animals with and without a tumor. We have investigated an additive model, which specifies that the difference in the two death rates is constant, and a multiplicative model, which specifies that the ratio of the two death rates is constant. Both of these models allow the transition rates to vary over time, and yet they do not require parametric models, lethality assumptions, cause-of-death data, or interim sacrifices. Computer simulations show that statistical tests based on these models perform well, especially the additive model.